Question

determine the standard form of the equation for the circle with center (h,k) = (0, -2) and radius r=9

Answer 1

Equation of circle

(x-h)^2+(y-k)^2=r^2
so lets put the values in,
h=0 and k=-2 and r=9

(x-0)^2 + (y+2)^2=81

x^2 + y^2 +4y +4 = 81

x^2 + y^2 +4y = 77

that's your Answer.

Answer 2

(x-h)^2+(y-k)^2=r^2
(x-0)^2+(y+2)^2=9^2
x^2+y^2+4+4y=81
x^2+y^2+4y-81+4=0
x^2+y^2+4y-77=0